无网格法在点弹性支承矩形薄板横向振动中的应用

基于薄板理论和弹性动力学Hamilton原理的推广,采用无网格伽辽金法,建立了具有有限多个点弹性支承的弹性矩形薄板横向振动的无量纲量运动微分方程,给出了其特征方程。通过求解特征方程,得出了四边简支板的无量纲固有频率随点弹性支承的刚性系数和支承位置的变化曲线,分析了点弹性支承的刚性系数和支承位置对矩形薄板横向振动特性的影响。数值计算结果表明,无网格法求解点弹性支承板横向振动问题是切实可行的。

Application of meshless method in the transverse vibration of rectangular thin plate with elastic point supports

Based on the thin plate theory and the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plate with finite elastic point supports are established by the element-free Galerkin method.The eigenvalue equations are presented.By solving the eigenvalue equations,the curves of dimensionless natural frequency of thin plate with four edges simply supported versus the rigid constant and locations of elastic point support are obtained.The effects of rigi...